Find the image of the point `(1, 6 ,3)` in the line `x/1=(y-1)/2=(z-2)/3.` Find the shortest distance between the lines; `vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk)`

Find the shortest distance between the lines : vecr=hati-hatj+lamda(2hati+hatk) and vecr=2hati-hatj+mu(hati+hatj-hatk)

Find the shortest distance between the lines vecr = hati+ hatj+hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+3hatk)

Find the shortest distance between the lines vecr = hati+ hatj+hatk+lambda(3hati-hatj) and vecr=4hati-hatk+mu(2hati+3hatk)

Find the shortest distance between the lines vecr =lambda (2hati+ 3hatj+4hatk) and vecr=(hati-hatj)+t(2hati-3hatj+4hatk)

Find the shortest distance between the lines vecr =lambda (2hati+ 3hatj+4hatk) and vecr=(hati-hatj)+t(2hati-3hatj+4hatk)

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by : vecr= (-4hati+4hatj+hatk)+lambda(hati+hatj-hatk) and vecr=(-3hati-8hatj-3hatk)+mu(2hati+3hatj+3hatk) .

Find the shortest distance between the lines vecr=(4hati-hatj)+lambda(hati+2hatj-3hatk) and vecr=(hati-hatj+2hatk)+mu(2hati+4hatj-5hatk) .

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by : vecr= (3hati+8hatj+3hatk)+lambda(3hati-hatj+hatk) and vecr=(-3hati-7hatj+6hatk)+mu(-3hati+2hatj+4hatk) .

Find the shortest distance between the lines vecr = (1-t)hati+(t-2)hatj+(3-2t)hatk and vecr = (s+1)hati+(2s-1)hatj-(2s+1)hatk

Find the shortest distance between the lines (x-6)/(3)=(y-7)/(-1)=(z-4)/(1) and vecr=-9hati+2hatk+t(-3hati +2hatj+4hatk) .